Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Abramowitz M, Stegun IA (1972) Handbook of Mathematical Functions. Dover, Mineola, New York
Bellin A, Rubin Y (1996) HYDRO_GEN: A spatially distributed random field generator for correlated properties. Stochastic Hydrology and Hydraulics (10), 253–278
Boufadel MC, Lu S, Molz FJ, Lavalle D (2000) Multifractal scaling of the intrinsic permeability. Water Resources Research 36, 3211–3222
Dagan G (1994) Significance of heterogeneity of evolving scales to transport in porous formations. Water Resources Research 30(12), 3327–3336
Desbarats AJ, Bachu S (1994) Geostatistical analysis of aquifer heterogeneity from the core scale to the basin scale: A case study. Water Resources Research 30(3), 673–684
Di Federico V, Neuman SP (1997) Scaling of random fields by means of truncated power variograms and associated spectra. Water Resources Research 33(5), 1075–1085
Di Federico V, Neuman SP (1998a) Flow in multiscale log conductivity fields with truncated power variograms. Water Resources Research 34(5), 975–987
Di Federico V, Neuman SP (1998b) Transport in multiscale log conductivity fields with truncated power variograms. Water Resources Research 34(5), 963–973
Di Federico V, Neuman SP, Tartakovsky DM (1999) Anisotropy, lacunarity, upscaled conductivity and its covariance in multiscale fields with truncated power variograms. Water Resources Research 35(10), 2891–2908
Eggleston J, Rojstaczer S (1998) Inferring spatial correlation of hydraulic conductivity from sediment cores and outcrops. Geophys. Res. Lett. 25(13), 2321–2324
Gelhar LW (1993) Stochastic Subsurface Hydrology. Prentice-Hall, Englewood Cliffs, New Jersey
Glimm J, Lindquist WB, Pereira F, Zhang Q (1993) A theory of macrodispersion for the scale-up problem. Transp. Porous Media 13(1), 97–122
Grindrod P, Impey MD (1992) Fractal field simulations of tracer migration within the WIPP Culebra Dolomite. Rep. IM2856-1, vers. 2, p. 62, Intera Inf. Technol., Denver, Colorado, March 1992
Guzman AG, Geddis AM, Henrich MJ, Lohrstorfer CF, Neuman SP (1996) Summary of Air Permeability Data From Single-Hole Injection Tests in Unsaturated Fractured Tuffs at the Apache Leap Research Site: Results of Steady-State Test Interpretation. Rep. NUREG/CR-6360, prepared for U.S. Nuclear Regulatory Commission, Washington, D.C.
Hewett TA (1986) Fractal distributions of reservoir heterogeneity and their influence on fluid transport. SPE Pap. 15386 presented at 61st Annual Technical Conference, Soc. Petrol. Engin., New Orleans, Los Angeles
Liu HH, Molz FJ (1996) Discrimination of fractional Brownian movement and fractional Gaussian noise structures in permeability and related property distribution with range analysis. Water Resources Research 32(8), 2601–2605
Liu HH, Molz FJ (1997) Multifractal analysis of hydraulic conductivity distributions. Water Resources Research 33(11), 2483–2488
Molz FJ, Boman GK (1993) A stochastic interpolation scheme in subsurface hydrology. Water Resources Research 29(11), 3769–3774
Molz FJ, Boman GK (1995) Further evidence of fractal structure in hydraulic conductivity distribution. Geophys. Res. Lett. 22(18), 2545–2548
Molz FJ, Liu HH, Szulga J (1997) Fractional Brownian motion and fractional Gaussian noise in subsurface hydrology: A review, presentation of fundamental properties, and extensions. Water Resources Research 33(10), 2273–2286
Molz FJ, Hewett TA, Boman GK (1998) A pseudo-fractal model for hydraulic properties in porous medium. In: Baveye P, Parlange J-Y, Stewart BA (eds) Fractals in Soil Sciences. CRC Press, Boca Raton, Fla, 341–372
Molz FJ, Rajaram H, Lu S (2003) Stochastic fractal-based models of heterogeneity in subsurface hydrology: Origins, applications, limitations, and future research questions. Reviews of Geophysics, in press
Neuman SP (1990) Universal scaling of hydraulic conductivities and dispersivities in geologic media. Water Resources Research 26(8), 1749–1758
Neuman SP (1994) Generalized scaling of permeabilities: Validation and effect of support scale. Geophys. Res. Lett. 21(5), 349–352
Neuman SP (1995) On advective transport in fractal velocity and permeability fields. Water Resources Research 31(6), 1455–1460
Neuman SP, Di Federico V (2003) The multifaceted nature of hydrogeologic scaling and its interpretation. Rev. Geophys., in press
Painter S (1996a) Evidence for non-Gaussian scaling behavior in heterogeneous sedimentary formations. Water Resources Research 32(5), 1183–1195
Painter S (1996b) Stochastic interpolation of aquifer properties using fractional Levy motion. Water Resources Research 32(5), 1323–1332
Painter S (1998) Numerical method for conditional simulation of Levy random fields. Math. Geol. 30(2), 163–179
Robin MJL, Sudicky EA, Gillham RW, Kachanoski RG (1991) Spatial variability on strontium distribution coefficients and their correlation with hydraulic conductivity in the Canadian Forces Base Borden aquifer. Water Resources Research 27(10), 2619–2632
Rubin Y, Bellin A (1998) Conditional Simulation of Geologic Media with Evolving Scales of Heterogeneity. In: Sposito G (ed), Scale Dependence and Scale Invariance in Hydrology, Cambridge University Press, 398–420
Tubman KM, Crane SD (1995) Vertical versus horizontal well log variability and application to fractal reservoir modeling. In: Barton CC, La Pointe PL (eds) Fractals in Petroleum Geology and Earth Processes. Plenum, New York, 279–293
Voss RF (1985) Random fractals: Characterization and measurement. In: Pynn R, Skjeltorp A (eds), Scaling Phenomena in Disordered Systems, NATO ASI Series, p. 133
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2005 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Cintoli, S., Neuman, S.P., Di Federico, V. (2005). Scaling Effects on Finite-Domain Fractional Brownian Motion. In: Geostatistics for Environmental Applications. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-26535-X_7
Download citation
DOI: https://doi.org/10.1007/3-540-26535-X_7
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-26533-7
Online ISBN: 978-3-540-26535-1
eBook Packages: Earth and Environmental ScienceEarth and Environmental Science (R0)